Finally we apply the methodology to the dataset provided by [1]}. This dataset contains 40 transmission pairs for which [1]} were reasonably sure that there was direct transmission within the pair. In their work the authors' interest was to estimate the generation time provided that they already have an estimate for the density of the incubation period (so the dataset was used in a slightly different context). Thus we can reasonably illustrate our methodology on this dataset: Semi-parametric estimation of features of the generation time and the incubation time. The dataset contains symptom onset dates for all transmission pairs, but the exposure window is not always reported. In that case we impute the dataset in the same way as [1]}: The beginning of the exposure window is at the earliest 60 days before symptom onset of the infector. The end of the infection window is at the latest the symptom onset time of any of the two people in the pair or the end of the exposure window of the second person which is reported in some cases. We stress that our interest lies in the theoretical analysis of the methodology and we provide here an illustration for how our methodology can be used. A complete data analysis would for example also require a robustness analysis against potential issues like the question whether the transmission pairs are random samples from the pandemic.
